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Cauchy formula for the time-varying linear systems with caputo derivative

  • Tadeusz Kaczorek EMAIL logo and Dariusz Idczak
Published/Copyright: April 28, 2017
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 20 Issue 2

Abstract

In the paper, existence, uniqueness and a Cauchy formula for the solution to a time-varying linear system containing fractional Caputo derivative is obtained. This formula shows that nonnegativity of the data of the system implies nonnegativity of the solution. In the context of a strenghthening of this result, an example illustrating the absence (in the case of Caputo derivative) of the standard relation “monotonicity of function - sign of derivative”.

MSC 2010: Primary 34A08; 26A33
Key Words and Phrases: fractional time-varying linear system; Caputo derivative; solution; positivity

References

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Received: 2016-9-7
Published Online: 2017-4-28
Published in Print: 2017-4-25

© 2017 Diogenes Co., Sofia

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  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 20–2–2017)
  4. Survey Paper
  5. The Chronicles of Fractional Calculus
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  7. A Numerical Study of the Homogeneous Elliptic Equation with Fractional Boundary Conditions
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  19. Invariant subspace method: A tool for solving fractional partial differential equations
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  21. Cauchy formula for the time-varying linear systems with caputo derivative
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  23. Overconvergence of series in generalized mittag-leffler functions
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https://doi.org/10.1515/fca-2017-0025
Keywords for this article
fractional time-varying linear system; Caputo derivative; solution; positivity

Articles in the same Issue

  1. Frontmatter
  2. Editorial Note
  3. FCAA related news, events and books (FCAA–Volume 20–2–2017)
  4. Survey Paper
  5. The Chronicles of Fractional Calculus
  6. Research Paper
  7. A Numerical Study of the Homogeneous Elliptic Equation with Fractional Boundary Conditions
  8. Research Paper
  9. A novel unstructured mesh finite element method for solving the time-space fractional wave equation on a two-dimensional irregular convex domain
  10. Research Paper
  11. Ulam stability for Hilfer type fractional differential inclusions via the weakly Picard operators theory
  12. Research Paper
  13. Determination of two unknown thermal coefficients through an inverse one-phase fractional Stefan problem
  14. Research Paper
  15. Fractional integral operators characterized by some new hypergeometric summation formulas
  16. Research Paper
  17. A high-order predictor-corrector method for solving nonlinear differential equations of fractional order
  18. Research Paper
  19. Invariant subspace method: A tool for solving fractional partial differential equations
  20. Research Paper
  21. Cauchy formula for the time-varying linear systems with caputo derivative
  22. Research Paper
  23. Overconvergence of series in generalized mittag-leffler functions
  24. Research Paper
  25. On a new class of constitutive equations for linear viscoelastic body
  26. Research Paper
  27. Observability for fractional diffusion equations by interior control
  28. Research Paper
  29. Null controllability of fractional dynamical systems with constrained control
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